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The Riccati Transfer Matrix Method
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1978
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Numerical AnalysisEngineeringMechanical EngineeringRotor DynamicStructural OptimizationComputational MechanicsMatrix TheoryModal AnalysisNumerical SimulationFlexible MemberTransfer MatricesMatrix MethodStructural DynamicStructural VibrationInverse ProblemsStructural MembersMatrix AnalysisMechanical SystemsStructural AnalysisStructural MechanicsVibration Control
The Riccati transfer matrix method is a new technique that leverages an extensive catalog of transfer matrices to analyze structural members, including rotating shafts. It eliminates numerical instability in high‑frequency, static, and long‑member analyses, halves computational time and storage, and its accuracy is confirmed by rotating‑shaft simulations.
The Riccati transfer matrix method is a new technique for analyzing structural members. This new technique makes use of an existing large catalog of transfer matrices for various structural members such as rotating shafts. The numerical instability encountered when calculating high resonant frequencies, static response of a flexible member on a stiff foundation, or the response of a long member by the transfer matrix method is eliminated by the Riccati transfer matrix method. The computational time and storage requirements of the Riccati transfer matrix method are about half the values for the transfer matrix method. A rotating shaft analysis demonstrates the numerical accuracy of the method.